According to MacTracker, all of the Late 2006 iMacs shipped with Mac OS X 10.4.7 or 10.4.8 (Tiger). There never were any retail Tiger discs for Intel-based Macs; the only Tiger DVD-ROMs are the recovery discs Apple shipped with these early Intel-based Macs.
None of the Late 2006 iMacs can run anything than Mac OS X 10.7.5 (Lion). Lion dropped support for Rosetta 1. You can run some Mac OS X / PowerPC applications on Intel-based Macs under Snow Leopard, using Rosetta 1 - but as of Lion, any application that is PowerPC-only simply won't run.
Lion is so old that you're unlikely to be able do much Web browsing with it, whether with Safari or with third-party browsers. It predates the move to stronger protocols for https security, so the available browsers probably won't even be able to connect to many Web sites. There have also been many changes to how Web sites display things, so even if you manage to connect to a few sites, you may not be able to display their contents properly.
We're also talking about iMacs with
- Two-core Core 2 Duo processors
- A maximum of 2 GB or 3 GB of RAM (depending on the model)
- Mechanical hard drives
- USB 2.0 ports
By now, many of the games that ran on those old Macs will have been pulled from the market. Those iMacs date from before the introduction of the Mac App Store, when most software developers shipped programs on optical discs. The Mac App Store has now almost completely killed off that method of distribution, and it looks like some older 32-bit games either never made it to the App Store, or have been pulled from the App Store.